Non-perturbative superpotentials across lines of marginal stability

TL;DR

This paper studies how non-perturbative superpotentials in 4d N=1 string compactifications behave near lines of marginal stability, revealing a continuity mechanism involving multi-instanton contributions and fermion zero mode lifting.

Contribution

It uncovers a novel non-perturbative mechanism ensuring superpotential continuity across stability lines through multi-instanton effects and zero mode interactions.

Findings

Superpotentials remain continuous despite BPS spectrum changes.

Multi-instanton contributions reconstruct single-instanton effects.

Fermion zero modes are lifted via interactions with other instantons.

Abstract

We discuss the behaviour of non-perturbative superpotentials in 4d N=1 type II compactifications (and orientifolds thereof) near lines of marginal stability, where the spectrum of contributing BPS D-brane instantons changes discontinuously. The superpotential is nevertheless continuous, in agreement with its holomorphic dependence on the closed string moduli. The microscopic mechanism ensuring this continuity involves novel contributions to the superpotential: As an instanton becomes unstable against decay to several instantons, the latter provide a multi-instanton contribution which reconstructs that of the single-instanton before decay. The process can be understood as a non-perturbative lifting of additional fermion zero modes of an instanton by interactions induced by other instantons. These effects provide mechanisms via which instantons with U(1) symmetry can contribute to the superpotential. We provide explicit examples of these effects for non-gauge D-brane instantons, and for D-brane gauge instantons (where the motions in moduli space can be interpreted as Higgsing, or Seiberg dualities).